2019 Advanced topics in Analysis H

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Ninomiya Syoiti 
Course component(s)
Lecture
Day/Period(Room No.)
Thr3-4(H137)  
Group
-
Course number
MTH.C504
Credits
1
Academic year
2019
Offered quarter
2Q
Syllabus updated
2019/3/18
Lecture notes updated
2019/7/29
Language used
English
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Course description and aims

In this lecture, the topics discussed in ``Advanced topics in analysis G'' are developed in continuous time models.

The following notions such as Ito integral, Stochastic Differential Equations, and some models in mathematical finance are discussed.

Student learning outcomes

Understanding the following notions:
Ito calculus and basic knowledge of stochastic differential equations

Keywords

Ito calculus, stochastic differential equation, mathematical finance

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Blackboard and handouts

Course schedule/Required learning

  Course schedule Required learning
Class 1 Ito integral (stochastic integral)(1), definition Details will be provided each class session.
Class 2 Ito integral (2), basic properties
Class 3 Ito formula
Class 4 Ito Representation theorem
Class 5 Stochastic Differential Equation (1), Existence of the solution
Class 6 Stochastic Differential Equation (2), Approximations of solutions
Class 7 Stochastic Differential Equation (3)
Class 8 Mathematical Finance

Textbook(s)

None in particular.

Reference books, course materials, etc.

Taniguchi, S., ``Stochastic Differential Equations,'' Kyoritsu
Kusuoka, S., ``Stochastic Analysis,'' Chisenshokan

Assessment criteria and methods

Based on reports. Details will be provided in the class.

Related courses

  • MTH.C361 : Probability Theory
  • MTH.C503 : Advanced topics in Analysis G

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None in particular

Other

None in particular

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